Singularity-free neural network controller with iterative training

A repetitive control scheme for trajectory tracking of a discrete nonlinear system is presented in this paper, where neural networks are used to approximate the unknown but repeatable nonlinearities. Contrary to the online adaptive training of neural networks, the neural networks are trained by tracking a trajectory multiple times so that the tracking performances of the whole trajectory can be improved through repetition. In order to avoid the singularity problem caused by the inverse of approximation of the coupling matrix, this paper modifies the neural network approximations of the coupling matrix and this modification does not cause control instability.